Method for controlling shrinkage of formed ceramic body

ABSTRACT

The present invention provides a method for controlling the shrinkage of formed ceramic bodies, by which it is possible to suppress fluctuation of the shrinkage of formed ceramic bodies and to cause the shrinkage to approximate the target rate. The method comprises controlling the shrinkage of formed ceramic bodies in manufacturing ceramic products by a predetermined manufacturing process from ceramic powder ground by a dry-type ball mill. Such control can be achieved by determining a correlation between the change in the amount of the ground ceramic powder taken out from the dry-type ball mill with elapse time and the shrinkage during firing of the formed ceramic body, and thereafter adjusting the manufacturing conditions based on the previously-determined conditions for the above-mentioned manufacturing process and the correlation with respect to the shrinkage obtained.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for controlling the shrinkageof a formed ceramic body during firing and, more particularly, to amethod for controlling the shrinkage of a formed ceramic body when aceramic product is manufactured by a predetermined manufacturing processfrom ceramic powder produced by grinding using a dry-type ball mill suchas Attritor.

2. Description of Related Art

To increase the accuracy of dimension and shape of finished products andto avoid defects in the shape and the like in the manufacture of ceramicproducts, it is important to control the degree of firing shrinkage whena formed body produced from a raw material such as a ceramic powder isfired to obtain a fired body. Particularly, in electronic parts such asICs and condensers, in which multi-layer ceramic substrates are used,controlling the shrinkage of green sheets for the multi-layer ceramicsubstrates is very important.

FIG. 5 is a process flow diagram showing a process for manufacturinggreen sheets for multi-layer ceramic substrates. In this manufacturingprocess, ceramic powder procured by purchasing and the like is groundusing attritor (hereinafter referred to as dry-type ball mill). Theground ceramic powder is taken out from the ball mill and treated withheat.

Next, a binder, a dispersant, a plasticizer, and the like are added tothe ground ceramic powder. Then, a liquid such as butanol is furtheradded and the resulting material is mixed using a trommel mixer.

The slurry obtained in this manner is molded into a formed body (a greensheet) with predetermined dimensions using a doctor blade formingmachine. The formed body is then dried and fired.

Conventionally, a commonly accepted method of controlling the firingshrinkage in the process for manufacturing ceramic products has been tosuppress fluctuation of the shrinkage by constantly employing fixedmanufacturing conditions (no specific prior art document has been foundon this subject). As specific manufacturing conditions in the processfor manufacturing green sheets, for example, heat treatment conditionsfor treating ground ceramic powder with heat (heating temperature,heating time, etc.), the composition of compounded ingredients (theamount of a dispersant, etc.), raw material mixing conditions (mixingtime, etc.), formed body drying conditions (temperature, air flow rate,etc.), press conditions (temperature, mass, etc.), formed body firingconditions (firing temperature, firing time, etc.), and the like can begiven. It has been a conventional practice to maintain all of theseconditions constant for controlling the shrinkage.

However, even if all of these conditions in the process of manufacturingceramic products are maintained constant, the shrinkage significantlyfluctuates according to the lot of ground ceramic powder to be used.Thus, it has been difficult to accurately control the shrinkage byconventional controlling methods.

The present invention has been completed in view of this situation andhas an object of providing a method for controlling the shrinkage offormed ceramic bodies, by which it is possible to suppress fluctuationof the shrinkage of formed ceramic bodies and to cause the shrinkage toapproximate the target rate.

SUMMARY OF THE INVENTION

According to the present invention, in a method of manufacturing ceramicproducts by a predetermined manufacturing process from ceramic powderground by a dry-type ball mill, a method for controlling the shrinkageof formed ceramic bodies comprising determining a correlation betweenthe change in the amount of the ground ceramic powder taken out from thedry-type ball mill with elapse time and the shrinkage during firing ofthe formed ceramic body, and thereafter adjusting the manufacturingconditions based on the previously-determined conditions for theabove-mentioned manufacturing process and the correlation with respectto the shrinkage obtained is provided.

According to another feature of the present invention, a method forcontrolling the shrinkage of formed ceramic bodies comprisingdetermining a shrinkage of formed ceramic bodies by manufacturing theceramic products by a predetermined manufacturing process from ceramicpowder ground using a dry-type ball mill, followed by firing,determining the correlation between the change in the mass of the groundceramic powder taken out from the dry-type ball mill over a fixed periodof time and the shrinkage, estimating the shrinkage of formed ceramicbodies based on the above correlation from the mass of the groundceramic powder taken out from the dry-type ball mill over apredetermined period of time, and partially adjusting the manufacturingconditions based on the previously-determined conditions for theabove-mentioned manufacturing process and the correlation with respectto the shrinkage obtained. to offset the difference between theestimated shrinkage and the target shrinkage is provided.

The shrinkage in the present invention is preferably the averageshrinkage determined by the following formula (1):Average shrinkage=(longitudinal shrinkage+lateral shrinkage+thicknessshrinkage)/3  (1)

-   -   wherein the longitudinal shrinkage is a value determined by the        following formula (2), the lateral shrinkage is a value        determined by the following formula (3), and the thickness        shrinkage is a value determined by the following formula (4).        Longitudinal shrinkage=longitudinal dimension before        firing/longitudinal dimension after firing  (2)        Lateral shrinkage=lateral dimension before firing/lateral        dimension after firing  (3)        Thickness shrinkage=thickness before firing/thickness after        firing  (4)

In the present invention, assuming that the elapse time required to takeout 90% by mass of ground ceramic powder from the dry-type ball millfrom the start of taking out the ground ceramic powder is 100, the abovemass of the ground ceramic powder taken out from the dry-type ball millis preferably the mass of the ground ceramic powder taken out during arelative elapse time of 75 to 100.

Furthermore, in the present invention, the equivalent spherical diameter(Rs) of the ceramic powder to be ground by the dry-type ball millrepresented by the formula Rs (μm)=6/ρS is preferably 1 μm or less,

-   -   wherein p is the true density (g/cm³) of the ceramic powder and        S is the BET specific surface area (m²/g) of the ceramic powder.

According to the controlling method of the present invention,fluctuation of the shrinkage of formed ceramic bodies can be suppressedand the shrinkage can be approximated to the target rate by measuringthe change in mass of the ground ceramic powder taken out from thedry-type ball mill with elapse of time and causing the measured resultsto be reflected in the manufacturing conditions. In this manner, theshrinkage of the formed ceramic body can be accurately controlled withease.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example of a graph obtained by plotting the averageshrinkage against the mass of ground ceramic powder taken out in arelative elapse time of 75 to 100.

FIG. 2 illustrates an example of a graph obtained by plotting theaverage shrinkage against the heat treatment temperature.

FIG. 3 illustrates an example of a graph obtained by plotting theaverage shrinkage against the amount of dispersant.

FIG. 4 illustrates an example of a graph obtained by plotting theaverage shrinkage against the mixing time of a trommel mixer.

FIG. 5 is a drawing showing an embodiment of a green sheet manufacturingprocess.

DETAILED DESCRIPTION OF THE EMBODIMENT

Specific embodiments of the controlling method according to the presentinvention will now be described. The present invention, however, shouldnot be construed as being limited to these embodiments. Variousalterations, modifications, and improvements are possible within thescope of the present invention by persons skilled in the art.

The present invention has been made based on the finding that whenmanufacturing a ceramic product using ceramic powder ground by adry-type ball mill, the temporal response of the amount of the ceramicpowder taken out from the dry-type ball mill has a certain correlationwith the degree of firing shrinkage (i.e., the shrinkage) of the formedbody produced using the ground ceramic powder.

Grinding of ceramic powder using a dry-type ball mill is significantlyaffected by environmental conditions and the like during processing. Forexample, the ceramic powder becomes moistened on a rainy day due to highhumidity and becomes less moistened on a fine day due to low humidity.This creates a variation in the ground conditions of ceramic powder(characteristic of ground ceramic powder) and causes temporalfluctuation in the amount of ceramic powder taken out from the dry-typeball mill. In grinding ceramic powder using a dry-type ball mill, balls(rotating balls) are put into the ball mill and rotated to agitate andgrind the ceramic powder. The balls are worn as grinding operations arerepeated, whereby the grinding conditions change and cause the temporalfluctuation in the amount of the taken out powder. In addition, when thegrinding operation is carried out twice a day, the temperature insidethe ball mill is higher in the second grinding operation than in thefirst operation.

Therefore, the fine particle characteristics of the ground ceramicpowder can be identified by measuring the above-mentioned temporalchange in the amount of ground ceramic powder taken out from the mill,specifically, the mass of the ground ceramic powder taken out from thedry-type ball mill with elapse of time. The fine particlecharacteristics herein include the form and particle size distributionof primary particles, the form and particle size distribution offlocculated particles, specific surface area, and the like. The fineparticle characteristics greatly affect the shrinkage of a formed body.

Therefore, the temporal response in the amount of ceramic powder takenout from the dry-type ball mill has a correlation with the degree offiring shrinkage, i.e. the shrinkage of the formed body. As a result ofextensive studies, the present inventors have found that, assuming thatthe period of time required to take out 90% by mass of ground ceramicpowder from the dry-type ball mill from the start of taking out of theground powder is 100, the mass of the ground ceramic powder taken outfrom the dry-type ball mill during a relative elapse time of 75 to 100greatly affects the shrinkage.

In the present invention, to identify the correlation between theshrinkage and the temporal response in the amount of the ceramic powdertaken out from the dry-type ball mill, the ceramic powder is groundusing a dry type ball mill and, using the ground ceramic powder thusobtained, a ceramic body is formed and fired by a manufacturing processunder specific conditions, and the correlation rate of the resultingformed body is determined.

There are various methods of specifying the shrinkage according to theform of the products and the like. Although there are no specificlimitations to the method of specifying the shrinkage in the presentinvention, the average shrinkage determined by the following formula (1)can be preferably employed, for example, when the formed ceramic body isa thin green sheet with a certain thickness. An embodiment using thefollowing average shrinkage as the shrinkage will be described in thefollowing description.Average shrinkage=(longitudinal shrinkage+lateral shrinkage+thicknessshrinkage)/3  (1)

-   -   wherein the longitudinal shrinkage is a value determined by the        following formula (2), the lateral shrinkage is a value        determined by the following formula (3), and the thickness        shrinkage is a value determined by the following formula (4).        Longitudinal shrinkage=longitudinal dimension before        firing/longitudinal dimension after firing  (2)        Lateral shrinkage=lateral dimension before firing/lateral        dimension after firing  (3)        Thickness shrinkage=thickness before firing/thickness after        firing  (4)

After determination of the actual shrinkage in the above-mentionedmanner, the correlation between the average shrinkage and the mass ofthe ground ceramic powder taken out from the dry-type ball mill during afixed period of time is determined. As the mass of the ground ceramicpowder taken out during the fixed period of time, the mass of the groundceramic powder taken out from the dry-type ball mill during a relativeelapse time of 75 to 100 is preferably used, provided that the period oftime required to take out 90% by mass of the charged ground ceramicpowder from the dry-type ball mill from the start of taking out of theground powder is 100. This is because the mass of the ground ceramicpowder taken out during the period of time in this range greatly affectsthe shrinkage as mentioned above.

To accurately identify the correlation rate, it is preferable to arrangefor easy determination of an estimated average shrinkage from the massof ground ceramic powder taken out during a fixed period of time byconducting the above-described operation two or more times whilechanging the mass of the ground ceramic powder taken out from thedry-type ball mill during the fixed period of time, for example, bychoosing the different circumstance (e.g. weather) in which the ceramicpowder is ground, and by producing a graph or formula based on theresults. For example, FIG. 1 shows an example of a graph obtained byplotting the average shrinkage against the mass of ground ceramic powdertaken out in a relative elapse time of 75 to 100.

After identifying the correlation between the average shrinkage and themass of a ground ceramic powder taken out over a fixed period of time, aceramic powder is processed in the same manner using the dry-type ballmill to obtain the ground ceramic powder. If the mass of the groundceramic powder to be taken out from the dry-type ball mill during thefixed period of time is determined, the average shrinkage which may beobtained when a ceramic body is formed from this ground ceramic powderand fired by the same manufacturing process as that used for identifyingthe above correlation can be estimated based on this correlation.

In the present invention, the average shrinkage, which may be obtainedwhen a ceramic body is formed from the above ground ceramic powder andfired by a certain manufacturing process at the time when the ceramicpowder is taken out from the dry-type ball mill, is estimated. Then, tooffset (correct) the difference between the estimated average shrinkageand the target average shrinkage, the operating conditions in the abovemanufacturing process are partially modified to control the averageshrinkage.

In this instance, any of the manufacturing conditions can be modifiedinasmuch as such modification changes the average shrinkage. Forexample, in the case of the process for manufacturing green sheets shownin FIG. 5, the average shrinkage can be changed by adjusting the heattreatment conditions of the ground ceramic powder, specifically, theheat treatment temperature and the heat treatment time. Note that theterm “heat treatment temperature” in the present specification means amaximum temperature among the temperatures used for treatment, and theterm “heat treatment time” means a duration period of keeping greensheets at the maximum temperature. The heat treatment time is from onehour to fifty hours, preferably from five hours to ten hours. FIG. 2shows an example of a graph obtained by plotting the average shrinkageagainst the heat treatment temperature. When the estimated averageshrinkage is smaller than the target average shrinkage, the differencebetween the estimated average shrinkage and the target average shrinkagecan be eliminated by increasing the heat treatment temperature to apredetermined level, whereby the resulting shrinkage is approximated tothe target average shrinkage. When the estimated average shrinkage ishigher than the target average shrinkage, the actual average shrinkagecan be approximated to the target average shrinkage by decreasing theheat treatment temperature to a predetermined level.

The above-mentioned green sheet can be produced by a wet forming method,in which a slurry for molding is obtained by adding additives such as abinder, a dispersant, and a plasticizer and a liquid such as butanol,and mixing them using a trommel mixer or the like. The followings aregiven as illustrative examples for the binder, the organic solvent, thedispersant, and the plasticizer useable in the present invention. Anybinder may be usable as far as it is soluble in an organic solvent,however, one may exemplify, as a preferable binder, polyvinyl butyrals,polyester methacrylic esters, ethyl cellulose, and the like. One mayexemplify, as an organic solvent, an alcohol such as methyl alcohol,ethyl alcohol, isopropyl alcohol, n-butyl alcohol, and the like; anaromatic hydrocarbon such as benzene, toluene, xylene and the like; aketone such as methyl ethyl ketone, methyl isobutyl ketone, acetone, andthe like; other common organic solvent such as trichloroethylene,tetrachloroethylene, and the like; and any mixture of the solventsmentioned above. One may exemplify, as a plasticizer, commonly usedplasticizers such as phthalate esters, sebacic esters, ethylene glycol,and the like. One may exemplify, as a dispersant, common dispersantssuch as sorbitan fatty acid esters, surfactants, and the like. Theaverage shrinkage can also be changed by adjusting the slurrycomposition. FIG. 3 shows an example of a graph obtained by plotting theaverage shrinkage against the amount of a dispersant. When the estimatedaverage shrinkage is smaller than the target average shrinkage, thedifference between the estimated average shrinkage and the targetaverage shrinkage can be eliminated by decreasing the amount of thedispersant in the slurry to a predetermined level, whereby the resultingshrinkage is approximated to the target average shrinkage. When theestimated average shrinkage is higher than the target average shrinkage,the actual average shrinkage can be approximated to the target averageshrinkage by increasing the amount of the dispersant in the slurry to apredetermined level.

Adjusting the mixing conditions when preparing the slurry for molding isanother preferred method for changing the average shrinkage. FIG. 4shows an example of a graph obtained by plotting the average shrinkageagainst the mixing time using a trommel mixer. When the estimatedaverage shrinkage is smaller than the target average shrinkage, thedifference between the estimated average shrinkage and the targetaverage shrinkage can be eliminated by decreasing the mixing time to apredetermined level, whereby the resulting shrinkage is approximated tothe target average shrinkage. When the estimated average shrinkage ishigher than the target average shrinkage, the actual average shrinkagecan be approximated to the target average shrinkage by increasing themixing time for a predetermined period of time.

Although there are no specific limitations to the formed ceramic bodyobtained by forming the ground ceramic powder produced by a dry-typeball mill, followed by firing, the green sheet produced by the wetforming method can be given as a preferable example. Such a green sheetcan be used for forming a multilayer ceramic substrate used formanufacturing electronic components such as ICs and condensers. Thestrict dimensional accuracy and shape accuracy required for suchelectronic components can be satisfied by precisely controlling theshrinkage according to the present invention.

Alumina, zirconia, silicon nitride, and the like can be used without anyspecific limitations as the ceramic in the present invention. Theparticles of ceramic powder obtained by grinding using the dry-type ballmill are preferably as small as 1 μm or less in terms of the equivalentspherical diameter (Rs). The Rs is still more preferably 0.05 to 0.6 μm.If the value of Rs is less than 0.05 μm, the particles undulyflocculate, making it difficult to smoothly grind the ceramic powder. Ifthe value of Rs is more than 0.6 μm, it takes a long time to grind theparticles, causing contamination of the ceramic powder with impuritiesfrom the mill balls.

The equivalent spherical diameter Rs is expressed by the followingformula.Rs (μm)=6/ρS

-   -   wherein ρ is the true density (g/cm³) of the ceramic powder and        S is the BET specific surface area (m²/g) of the ceramic powder.

Here, the true density (ρ) of the ceramic powder is a theoreticaldensity and is 6.10 g/cm³ in the case of partially stabilized zirconiapowder containing 3 mol % of yttria and 3.98 g/cm³ in the case ofalumina powder.

EXAMPLES

The present invention is described below in detail by examples.

Example 1

A 50 l dry-type ball mill (Attritor Type-D, manufactured by MitsuiMining. Co., Ltd.) was charged with 13 kg of partially stabilizedzirconia powder (3YSE manufactured by Tosoh Corp., Y₂O₃: 5.15% by mass,Al₂O₃: 0.25% by mass, BET specific surface area: 7.0 m²/g). The mixturewas ground for 15 minutes at a rotation of 220 rpm using 120 kg ofzirconia balls. As a grinding adjuvant, 15 g of oleic acid ester ofpolyethylene glycol (Polynon 0-44, manufactured by Tetsuno Yuka Co.,Ltd.) was added. After grinding, the bottom lid of the dry-type ballmill was opened while rotating the stirring wings to take out the groundpowder. The temporal response of the mass of taken out ground powder isshown in Table 1. It took eight minutes after the start of the grindingoperation to take out 90% by mass of the ground powder of the partiallystabilized zirconia powder put into the dry-type ball mill. The timerequired for taking out of the ground powder indicated in theparentheses in Table 1 is a relative elapse time when the time forremoving 90% by mass of the ground powder of the partially stabilizedzirconia powder put into the ball mill after eight minutes after thestart of the grinding operation was assumed to be 100. Six to eightminutes, for example, correspond to a relative elapse time of 75 to 100.TABLE 1 Time 0-2 2-4 4-6 6-8 8-10 minutes minutes minutes minutesminutes (0-25) (25-50) (50-75) (75-100) Amount 4.51 kg 3.79 kg 2.30 kg1.60 kg 0.20 kg

Prior to the above-mentioned grinding processing, a grinding process wascarried out separately two times using partially stabilized zirconiapowder of the same lot and the same dry-type ball mill (grinding processA and grinding process B). The mass of ground powder taken out in arelative elapse time of 75 to 100 was measured. The results are shown inTable 2. Green sheets were produced from the ground powders obtained inthe grinding process A and grinding process B according to themanufacturing process shown in FIG. 5. The resulting average shrinkagesare shown in Table 2. The manufacturing process details are as follows.

The partially stabilized zirconia powder was ground using a dry-typeball mill and filled into a capsule made of mullite. The capsule wasplaced in a kiln to heat the ground powder at 650° C. for ten hours. 100parts by mass of the heat-treated powder, 7.6 parts by mass of polyvinylbutyral resin, 3.8 parts by mass of di-2-ethylhexyl phthalate, 2.0 partsby mass of a sorbitan dispersant, 34.0 parts by mass of xylene, and 34.0parts by mass of 1-butanol were mixed together with zirconia balls in atrommel mixer for 30 hours. A green sheet with a dry thickness of 150 μmwas prepared from the resulting slurry on a polyethylene terephthalatesubstrate film using a doctor-blade molding machine. Test specimens witha 70 mm×70 mm dimension punched from the resulting green sheet wereplaced in a kiln and fired in air at 1450° C. for two hours. Thedimensions (length, width, and thickness) of the resulting fired bodywere measured to calculate the average shrinkage using theabove-mentioned formula (1). TABLE 2 Amount taken out in a 75-100 unitperiod Average shrinkage Grinding process A 2.15 kg 1.2576 Grindingprocess B 0.49 kg 1.2623

Based on the results shown in Table 2, the correlation between theaverage shrinkage and the mass of ground powder taken out in a relativeelapse time of 75 to 100 can be expressed by a linear function of thefollowing formula (5).Average shrinkage=−2.83×10⁻³×(amount taken out in a 75-100 unit time(kg))+1.2637  (5)

Since the mass of the ground powder taken out in a relative elapse timeof 75 to 100 in the first grinding process in this Example is 1.60 kg,as shown in Table 1, assuming that a green sheet is produced from theground powder obtained in this grinding process by the samemanufacturing process as above, the average shrinkage of the green sheetis estimated to be 1.2592 from the following formula (6).Average shrinkage=−2.83×10⁻³×(1.60)+1.2637=1.2592  (6)

Here, when the target average shrinkage is 1.261, the difference betweenthe target average shrinkage and the above average shrinkage is offset(corrected) by changing the temperature at which the ground powder istreated with heat. The relationship between the average shrinkage andthe heat treatment temperature is shown by the following formula (7).Average shrinkage=+7.26×10⁻⁵×(heat treatment temperature (° C.))+b  (7)

-   -   wherein b is a constant.

Because the estimated average shrinkage of the green sheet obtained bythe above manufacturing process, in which the heat treatment temperatureof 650° C. is employed, is 1.2592, to increase this average shrinkage to1.2610, the heat treatment temperature should be increased to 675° C. ascan be calculated from the following formulas (8) and (9). In anexperiment of producing a green sheet by changing the heat treatmenttemperature from 650° C. to 675° C. in the above manufacturing process,an average shrinkage of 1.2611 was achieved, confirming that the ratewas almost the same as the target average shrinkage.1.2592=+7.26×10⁻⁵×(650)+b  (8)1.2610=+7.26×10⁻⁵×(heat treatment temperature (° C.))+b  (9)

Example 2

A 50 l dry-type ball mill (Type-D, manufactured by Mitsui Mining. Co.,Ltd.) was charged with 13 kg of partially stabilized zirconia powder(3YSE manufactured by Tosoh Corp., Y₂O₃: 5.15% by mass, Al₂O₃: 0.25% bymass, BET specific surface area: 7.1 m²/g). The mixture was ground for15 minutes at a rotation of 220 rpm using 120 kg of zirconia balls. As agrinding adjuvant, 15 g of oleic acid ester of polyethylene glycol(Polynon 0-44, manufactured by Tetsuno Yuka Co., Ltd.) was added. Aftergrinding, the bottom lid of the dry-type ball mill was opened whilerotating the stirring wings to take out the ground powder. The temporalresponse of the mass of the taken out ground powder is shown in Table 3.The time required for taking out of the ground powder indicated in theparentheses in Table 3 is a relative elapse time when the time fortaking out 90% by mass of the ground powder of the partially stabilizedzirconia powder put into the ball mill was assumed to be 100. TABLE 3Time (0-25) (25-50) (50-75) (75-100) Amount 4.41 kg 3.70 kg 2.19 kg 1.70kg

Since the mass of ground powder taken out in a relative elapse time of75 to 100 in this grinding process is 1.70 kg, as shown in Table 3,assuming that a green sheet is produced from the ground powder obtainedin this grinding process by the same manufacturing process as above,based on the correlation of formula (5) in Example 1, the averageshrinkage of the green sheet is estimated to be 1.2589 from thefollowing formula (10).Average shrinkage=−2.83×10⁻³×(1.70)+1.2637=1.2589  (10)

Here, when the target average shrinkage is 1.261, the difference betweenthe target average shrinkage and the above estimated average shrinkageis offset (corrected) by changing the amount of a dispersant. Therelationship between the average shrinkage and the amount of dispersantis shown by the following formula (11).Average shrinkage=−3.1×10⁻³×(amount of dispersant (% by mass))+C  (11)

-   -   wherein C is a constant.

Because the estimated average shrinkage of the green sheet obtained bythe above manufacturing process, in which the amount of the dispersantused is 2.0% by mass, is 1.2589, to increase this average shrinkage to1.2610, the amount of the dispersant should be decreased to 1.3% by massas can be calculated from the following formulas (12) and (13). In anexperiment of producing a green sheet by changing the amount ofdispersant from 2.0% by mass to 1.3% by mass in the above manufacturingprocess, the average shrinkage of 1.2609 was achieved, confirming thatthe rate was almost the same as the target average shrinkage.1.2589=−3.1×10⁻³×(2.0)+C  (12)1.2610=−3.1×10⁻³×(amount of dispersant (% by mass))+C  (13)

Example 3

A 50 l dry-type ball mill (Type-D, manufactured by Mitsui Mining. Co.,Ltd.) was charged with 13 kg of partially stabilized zirconia powder(3YSE manufactured by Tosoh Corp., Y₂O₃: 5.15% by mass, Al₂O₃: 0.25% bymass, BET specific surface area: 6.8 m²/g). The mixture was ground for15 minutes at a rotation of 220 rpm using 120 kg of zirconia balls. As agrinding adjuvant, 15 g of oleic acid ester of polyethylene glycol(Polynon 0-44, manufactured by Tetsuno Yuka Co., Ltd.) was added. Aftergrinding, the bottom lid of the dry-type ball mill was opened whilerotating the stirring wings to take out the ground powder. The temporalresponse of the mass of taken out ground powder is shown in Table 4. Thetime required for taking out of the ground powder indicated in theparentheses in Table 4 is a relative elapse time when the time forremoving 90% by mass of the ground powder of the partially stabilizedzirconia powder put into the ball mill was assumed to be 100. TABLE 4Time (0-25) (25-50) (50-75) (75-100) Amount 4.80 kg 4.10 kg 2.60 kg 0.75kg

Since the mass of ground powder taken out in a relative elapse time of75 to 100 in this grinding process is 0.75 kg, as shown in Table 4,assuming that a green sheet is produced from this ground powder by thesame manufacturing process as above, the average shrinkage of the greensheet is estimated to be 1.2616 from the following formula (14), if thecorrelation of formula (5) in Example 1 is applied.Average shrinkage=−2.83×10⁻³×(0.75)+1.2637=1.2616  (14)

Here, when the target average shrinkage is 1.261, the difference betweenthe target average shrinkage and the above estimated average shrinkageis offset (corrected) by changing the mixing time of a trommel mixer.The relationship between the average shrinkage and the mixing time usinga trommel mixer is shown by the following formula (15).Average shrinkage=−8.33×10⁻⁵×(mixing time (hour))+d  (15)

-   -   wherein d is a constant.

Because the estimated average shrinkage of the green sheet obtained bythe above manufacturing process is 1.2617 when the mixing time of thetrommel mixer is 30 hours, to decrease this average shrinkage to 1.2610,the mixing time of the trommel mixer should be increased to 37.2 hoursaccording to the following formulas (16) and (17). In an experiment ofproducing a green sheet by increasing the mixing time of the trommelmixer from 30 hours to 37.2 hours in the above manufacturing process, anaverage shrinkage of 1.2610 was achieved, confirming that the rate wasthe same as the target average shrinkage.1.2616=−8.33×10⁻⁵×(30)+d  (16)1.2610=−8.33×10⁻⁵×(mixing time (hour))+d  (17)

Example 4

A 5 l dry-type ball mill (Type-D, manufactured by Mitsui Mining. Co.,Ltd.) was charged with 1.3 kg of partially stabilized zirconia powder(3YSE manufactured by Tosoh Corp., Y₂O₃: 5.15% by mass, Al₂O₃: 0.25% bymass, BET specific surface area: 7.2 m²/g). The mixture was ground for15 minutes at a rotation of 220 rpm using 12 kg of zirconia balls. As agrinding adjuvant, 1.5 g of oleic acid ester of polyethylene glycol(Polynon 0-44, manufactured by Tetsuno Yuka Co., Ltd.) was added. Aftergrinding, the bottom lid of the dry-type ball mill was opened whilerotating the stirring wings to take out the ground powder. The temporalresponse of the mass of taken out ground powder is shown in Table 5. Thetime required for taking out of the ground powder indicated in theparentheses in Table 5 is a relative elapse time when the time forremoving 90% by mass of the ground powder of the partially stabilizedzirconia powder put into the ball mill was assumed to be 100. TABLE 5Time (0-25) (25-50) (50-75) (75-100) Amount 0.46 kg 0.39 kg 0.24 kg 0.17kg

Prior to the above-mentioned grinding processing, a grinding process wascarried out separately two times using the same partially stabilizedzirconia powder and the same dry-type ball mill (grinding process C andgrinding process D). The mass of ground powder taken out in a relativeelapse time of 75 to 100 was measured. The results are shown in Table 6.Green sheets were produced from the ground powders obtained in thegrinding process C and grinding process D according to the manufacturingprocess shown in FIG. 5. The resulting average shrinkages are shown inTable 6. The manufacturing process details are as follows.

The partially stabilized zirconia powder was ground using a dry-typeball mill and filled into a capsule made of mullite. The capsule wasplaced in a kiln to heat the ground powder at 650° C. for ten hours. 100parts by mass of the heat-treated powder, 7.6 parts by mass of polyvinylbutyral resin, 3.8 parts by mass of di-2-ethylhexyl phthalate. 2.0 partsby mass of a sorbitan dispersant, 34.0 parts by mass of xylene, and 34.0parts by mass of 1-butanol were mixed together with zirconia balls in atrommel mixer for 30 hours. A green sheet with a dry thickness of 150 μmwas prepared from the resulting slurry on a polyethylene terephthalatesubstrate film using a doctor-blade molding machine. Test specimens witha 70 mm×70 mm dimension punched from the resulting green sheet wereplaced in a kiln and fired in air at 1450° C. for two hours. Thedimensions (length, width, and thickness) of the resulting fired bodywere measured to calculate the average shrinkage using theabove-mentioned formula (1). TABLE 6 Amount taken out in a 75-100 unitperiod Average shrinkage Grinding process C 0.23 kg 1.2570 Grindingprocess D 0.05 kg 1.2618

Based on the results shown in Table 6, the correlation between theaverage shrinkage and the mass of ground powder taken out in a relativeelapse time of 75 to 100 can be expressed by a linear function of thefollowing formula (18).Average shrinkage=−2.67×10⁻²×(amount taken out in a 75-100 unit time(kg))+1.2631  (18)

Since the mass of the ground powder taken out in a relative elapse timeof 75 to 100 in the first grinding process in this Example is 0.17 kg,as shown in Table 5, assuming that a green sheet is produced from thisground powder by the same manufacturing process as above, the averageshrinkage of the green sheet is estimated to be 1.2586 from thefollowing formula (19).Average shrinkage=−2.67×10⁻²×(0.17)+1.2631=1.2586  (19)

Here, when the target average shrinkage is 1.261, the difference betweenthe target average shrinkage and the above average shrinkage is offset(corrected) by changing the temperature when the ground powder istreated with heat. The relationship between the average shrinkage andthe heat treatment temperature is shown by the above formula (7).

Because the estimated average shrinkage of the green sheet obtained bythe above manufacturing process, in which the heat treatment temperatureof 650° C. is employed, is 1.2586, to increase this average shrinkage to1.2610, the heat treatment temperature should be increased to 683° C. ascan be calculated from the following formulas (20) and (21). In anexperiment of producing a green sheet by changing the heat treatmenttemperature from 650° C. to 683° C. in the above manufacturing process,the average shrinkage of 1.2608 was achieved, confirming that the ratewas almost the same as the target average shrinkage.1.2586=+7.26×10⁻⁵×(650)+b  (20)1.2610=+7.26×10⁻⁵×(Heat treatment temperature)+b  (21)

Example 5

A 50 l dry-type ball mill (Type-D, manufactured by Mitsui Mining. Co.,Ltd.) was charged with 8.45 kg of alumina powder (AL-150GS-3manufactured by Showa Denko, Co., Ltd., Al₂O₃: 99.5% by mass, BETspecific surface area: 6.4 m²/g). The mixture was ground for 15 minutesat a rotation of 220 rpm using 120 kg of zirconia balls. As a grindingadjuvant, 10 g of oleic acid ester of polyethylene glycol (Polynon 0-44,manufactured by Tetsuno Yuka Co., Ltd.) was added. After grinding, thebottom lid of the dry-type ball mill was opened while rotating thestirring wings to take out the ground powder. The temporal response ofthe mass of the taken out ground powder is shown in Table 7. The timerequired for taking out the ground powder indicated in the parenthesesin Table 7 is a relative elapse time when the time for removing 90% bymass of the ground powder of the alumina powder put into the ball millwas assumed to be 100. TABLE 7 Time (0-25) (25-50) (50-75) (75-100)Amount 2.93 kg 2.46 kg 1.50 kg 1.04 kg

Prior to the above-mentioned grinding processing, a grinding process wascarried out separately two times using the same alumina powder and thesame dry-type ball mill (grinding process E and grinding process F). Themass of ground powder taken out in a relative elapse time of 75 to 100was measured. The results are shown in Table 8. Green sheets wereproduced from the ground powders obtained in the grinding process E andgrinding process F according to the manufacturing process shown in FIG.5. The resulting average shrinkages are shown in Table 8. Themanufacturing process details are as follows.

The alumina powder Was ground using a dry-type ball mill and filled in acapsule made of mullite. The capsule was placed in a kiln to heat theground powder at 700° C. for one hour. 100 parts by mass of theheat-treated powder, 11.0 parts by mass of polyvinyl butyral resin, 5.5parts by mass of dioctyl phthalate, 2.0 parts by mass of a sorbitandispersant, 55.0 parts by mass of xylene, and 55.0 parts by mass of1-butanol were mixed together with zirconia balls in a trommel mixer for30 hours. A green sheet with a dry thickness of 150 μm was prepared fromthe resulting slurry on a polyethylene terephthalate substrate filmusing a doctor-blade molding machine. Test specimens with a 70 mm×70 mmdimension punched from the resulting green sheet were placed in a kilnand fired in air at 1400° C. for two hours. The dimensions (the length,width, and thickness) of the resulting fired body were measured tocalculate the average shrinkage using the above-mentioned formula (1).TABLE 8 Amount taken out in a 75-100 unit period Average shrinkageGrinding process E 1.40 kg 1.2341 Grinding process F 0.32 kg 1.2356

Based on the results shown in Table 8, the correlation between theaverage shrinkage and the mass of ground powder taken out in a relativeelapse time of 75 to 100 can be expressed by a linear function of thefollowing formula (22).Average shrinkage=−1.39×10⁻³×(amount taken out in a 75-100 unit time(kg))+1.2360  (22)

Since the mass of ground powder taken out in a relative elapse time of75 to 100 in the first grinding process in this Example is 1.04 kg, asshown in Table 7, assuming that a green sheet is produced from theground powder obtained in this grinding process by the samemanufacturing process as above, the average shrinkage of the green sheetis estimated to be 1.2346 from the following formula (23).Average shrinkage=−1.39×10⁻³×(1.04)+1.2360=1.2346  (23)

Here, when the target average shrinkage is 1.2300, the differencebetween the target average shrinkage and the above estimated averageshrinkage is offset (corrected) by changing the temperature when theground powder is treated with heat. The relationship between the averageshrinkage and the heat treatment temperature is shown by the followingformula (24).Average shrinkage=−3.65×10⁻⁵×(heat treatment temperature (° C.))+e  (24)

-   -   wherein e is a constant.

Because the estimated average shrinkage of the green sheet obtained bythe above manufacturing process, in which the heat treatment temperatureof 700° C. is employed, is 1.2346, to decrease this average shrinkage to1.2300, the heat treatment temperature should be increased to 826° C. ascan be calculated from the following formulas (25) and (26). In anexperiment of producing a green sheet by changing the heat treatmenttemperature from 700° C. to 826° C. in the above manufacturing process,the average shrinkage of 1.2301 was achieved, confirming that the ratewas almost the same as the target average shrinkage.1.2346=−3.65×10⁻⁵×(700)+e  (25)1.2300=−3.65×10⁻⁵×(Heat treatment temperature)+e  (26)

The present invention can be suitably used for controlling the shrinkagewhich is an indication of firing shrinkage when a fired body is obtainedby firing a formed ceramic body in the manufacture of ceramic products.The method can be suitably used for forming a multilayer ceramicsubstrate which is used for manufacturing electronic components such asICs and condensers, which require strict dimensional accuracy and shapeaccuracy.

1. A method for controlling the shrinkage of formed ceramic bodies whenmanufacturing ceramic products by a predetermined manufacturing processfrom a ceramic powder ground using a dry-type ball mill, comprisingdetermining a correlation between the change in the amount of the groundceramic powder taken out from the dry-type ball mill with elapse timeand the shrinkage during firing of the formed ceramic body, andthereafter adjusting the manufacturing conditions based on thepreviously-determined conditions for the above-mentioned manufacturingprocess and the correlation with respect to the shrinkage obtained.
 2. Amethod for controlling the shrinkage of formed ceramic bodies comprisingdetermining a shrinkage of formed ceramic bodies by manufacturing theceramic products by a predetermined manufacturing process from ceramicpowder ground using a dry-type ball mill followed by firing, determiningthe correlation between the change in the mass of the ground ceramicpowder taken out from the dry-type ball mill over a fixed period of timeand the shrinkage, estimating the shrinkage of formed ceramic bodiesbased on the above correlation from the mass of the ground ceramicpowder taken out from the dry-type ball mill over a predetermined periodof time, and partially adjusting the manufacturing conditions based onthe previously-determined conditions for the above-mentionedmanufacturing process and the correlation with respect to the shrinkageobtained. to offset the difference between the estimated shrinkage andthe target shrinkage.
 3. The method according to claim 1, wherein theshrinkage is determined using the following formula (1),Average shrinkage=(longitudinal shrinkage+lateral shrinkage+thicknessshrinkage)/3  (1) wherein the longitudinal shrinkage is a valuedetermined by the following formula (2), the lateral shrinkage is avalue determined by the following formula (3), and the thicknessshrinkage is a value determined by the following formula (4),Longitudinal shrinkage=longitudinal dimension before firing/longitudinaldimension after firing  (2)Lateral shrinkage=lateral dimension before firing/lateral dimensionafter firing  (3)Thickness shrinkage=thickness before firing/thickness after firing  (4).4. The method according to claim 2, wherein the shrinkage is determinedusing the following formula (1),Average shrinkage=(longitudinal shrinkage+lateral shrinkage+thicknessshrinkage)/3  (1) wherein the longitudinal shrinkage is a valuedetermined by the following formula (2), the lateral shrinkage is avalue determined by the following formula (3), and the thicknessshrinkage is a value determined by the following formula (4),Longitudinal shrinkage=longitudinal dimension before firing/longitudinaldimension after firing  (2)Lateral shrinkage=lateral dimension before firing/lateral dimensionafter firing  (3)Thickness shrinkage=thickness before firing/thickness after firing  (4).5. The method according to claim 2, wherein the mass of the groundceramic powder taken out from the dry-type ball mill is equivalent tothe mass of the ground ceramic powder taken out during a relative elapsetime of 75 to 100, provided that the period of time required to take out90% by mass of ground ceramic powder from the dry-type ball mill fromthe start of taking out the ground powder is
 100. 6. The methodaccording to claim 1, wherein part of the manufacturing conditions to bemodified is heat treatment conditions of the ground ceramic powder. 7.The method according to claim 2, wherein part of the manufacturingconditions to be modified is heat treatment conditions of the groundceramic powder.
 8. The method according to claim 1, wherein the formedceramic body is a green sheet molded by a wet method.
 9. The methodaccording to claim 2, wherein the formed ceramic body is a green sheetmolded by a wet method.
 10. The method according to claim 6, whereinpart of the manufacturing conditions to be modified is the compositionof slurry used in the wet molding method.
 11. The method according toclaim 7, wherein part of the manufacturing conditions to be modified isthe composition of slurry used in the wet molding method.
 12. The methodaccording to claim 6, wherein part of the manufacturing conditions to bemodified is the mixing conditions of the slurry used in the wet moldingmethod.
 13. The method according to claim 7, wherein part of themanufacturing conditions to be modified is the mixing conditions of theslurry used in the wet molding method.
 14. The method according to claim1, wherein the ceramic powder charged into the dry-type ball mill has anequivalent spherical diameter (Rs) represented by the formula Rs(μm)=6/ρS of 1 μm or less, wherein ρ is the true density (g/cm³) of theceramic powder and S is the BET specific surface area (m²/g) of theceramic powder.
 15. The method according to claim 2, wherein the ceramicpowder charged into the dry-type ball mill has an equivalent sphericaldiameter (Rs) represented by the formula Rs (μm)=6/ρS of 1 μm or less,wherein ρ is the true density (g/cm³) of the ceramic powder and S is theBET specific surface area (m²/g) of the ceramic powder.